Hi there,
I am going out on a limb and speculating that your elusive Patrick Kinsela came to NSW as part of either the Royal Staff Corps or more likely as part of the detachment of the 40th Regiment on foot, arriving on the same vessel as the then incoming Governor, Ralph Darling. The newspaper cutting clearly notes both those military groups arriving with Gov Darling.
Further, I am speculating that your chap took his discharge around 1829 and took it in NSW, and found employment as a Constable, so that by 1838 he was elevated to the position of Chief Constable....
Now, how to go about confirming or repudiating that speculation ....
Some suggestions .... the various regiments were on three and six year tours of duty .... to the various outposts in the growing Empire ... often as garrison forces .... guards policing the regulations of the various colonies etc... Some tours were for Ireland, others at The Cape, NSW, VDL, India etc...
Even Privates in the regiments were noted on various musters, pay rolls etc .... so these records are usually extant .... but are usually at Kew .... The National Archives (of the UK) ... there's online indexes at this link,
http://www.nationalarchives.gov.uk/a2a/ and the files are usually prefixed WO (War Office), but my understanding from here in NSW is that the files are very difficult to follow, particularly IF the person enlisted in one regiment and then transferred to another. (Of course, this may be the case with Patrick .... but I think he was in the 40th when Darling arrived. Perhaps he transferred to the 39th when the 40th departed NSW (for India ??) in 1829 .... not sure .... I have not found the time to investigate further, and may not have the time for several months.
However, if you can get to the National Library in Canberra you may well find duplicate film of the various reels that are part of the NSW State Records Office holdings... Or perhaps there's more to be found at the State Library in Sydney ... but under Sir Ralph Darling's papers rather than Bourke's ...

I can confirm though that his police uniform would most likely be that of the Red Coat variety ...

Cheers, JM